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C₂×#12934 #494276

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,14,9,15,8,13)(5,16,19,28,20,31,18,11)(6,21,23,30,25,29,24,12)(10,22,26,17,27,33,32,34);(3,5)(4,10,15,27)(6,22)(7,18)(8,19)(9,20)(11,12,28,30)(13,26,14,32)(16,29,31,21)(17,24)(23,34)(25,33);(3,5)(4,11)(6,17)(7,19)(8,18)(9,20)(10,12)(13,31)(14,16)(15,28)(21,26)(22,24)(23,33)(25,34)(27,30)(29,32)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401472);